The complex of free factors of a free group
Allen Hatcher, Karen Vogtmann
TL;DR
This paper revises a previous proof regarding the homotopy type of the geometric realization of proper free factors in a free group, confirming it is homotopy equivalent to a wedge of spheres.
Contribution
It corrects an earlier proof while establishing that the geometric realization of proper free factors is homotopy equivalent to a wedge of spheres.
Findings
The main theorem remains valid after correction.
The geometric realization is homotopy equivalent to a wedge of spheres.
The dimension of the spheres is n-2.
Abstract
This paper corrects an error in a proof in the original version of the paper published in 1998 in the Oxford Quarterly. The main theorem remains the same: The geometric realization of the partially ordered set of proper free factors in a finitely generated free group of rank is homotopy equivalent to a wedge of spheres of dimension .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis · Advanced Topology and Set Theory